Most people feel the altitude in Quito, but don't usually suffer any serious problems other than getting out of breath more easily. But of course, no-one can give guarantees about how any one individual will react. One common problem is that people arrive dehydrated off the flight, and then don't drink enough to counter the dehydrating effects of altitude, so it just keeps getting worse. The symptoms are similar. Some people do take Diamox for a short visit. You would need to bring it with you though, it's not easy to find in Quito although the Fybeca in the basement of QuiCentro Norte sometimes has it. Personally, I think it's overkill below 3,000m, but if you are very worried about it, it might be worth it. You might want to avoid the Teleferico as well.
Moving between the Amazon, Galapagos and Quito won't make much difference unless you are staying a few days in Quito, then going down to sea level and then coming back up for a few days. In which case you will lose any acclimatization you had in between. From Quito, cloud forest trips are usually to Mindo, which is much lower than Quito (less than 1,300m). Altitude wouldn't be an issue there.
Coca tea will trigger a positive for cocaine. There have been a few studies on it, and I can probably dig some references out if you are really interested. As far as I can recall, one cup led to a positive for about 20-30 hours, 2 cups were still positive after 52 hours, which was the longest period they tested.